oblicz PC i V stożka wiedzac ze tworzaca ma 8 cm a wysokość 4 cm
zad
H =4cm
l=8cm
liczymy promień r stozka z tw,Pitagorasa:
H²+r²=l²
4²+r²=8²
16+r²=64
r²=64-16
r=√48=√3·√16=4√3cm
objetosc stozka:
V=⅓πr²·H=⅓π·(4√3)²·4=⅓π·192=64πcm³
pole:
Pc=πr²+πrl=π·(4√3)²+π·4√3·8=48π+32√3π=16π(3+2√3)cm²
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zad
H =4cm
l=8cm
liczymy promień r stozka z tw,Pitagorasa:
H²+r²=l²
4²+r²=8²
16+r²=64
r²=64-16
r=√48=√3·√16=4√3cm
objetosc stozka:
V=⅓πr²·H=⅓π·(4√3)²·4=⅓π·192=64πcm³
pole:
Pc=πr²+πrl=π·(4√3)²+π·4√3·8=48π+32√3π=16π(3+2√3)cm²